VECTOR_DISTANCE
Purpose
VECTOR_DISTANCE
is the main function that you can use to calculate the distance between two vectors.
VECTOR_DISTANCE
takes two vectors as parameters. You can optionally specify a distance metric to calculate the distance. If you do not specify a distance metric, then the default distance metric is Cosine distance.
You can optionally use the following shorthand vector distance functions:

L1_DISTANCE

L2_DISTANCE

COSINE_DISTANCE

INNER_PRODUCT
All the vector distance functions take two vectors as input and return the distance between them as a BINARY_DOUBLE
.
VECTOR_DISTANCE
to perform a similarity search:

If you do not specify a distance metric, then the default distance metric
COSINE
is used for both exact and approximate (indexbased) searches. 
If you specify a distance metric that conflicts with the distance metric specified in a vector index, then the distance metric that you specify is used to perform the exact search.

If you specify a distance metric that matches the distance metric specified in a vector index, then distance metric specified in the vector index is used for both exact and approximate (indexbased) searches.
Parameters

expr1
andexpr2
must evaluate to vectors and have the same number of dimensions. This function returns NULL if eitherexpr1
orexpr2
is NULL or if the dimensions between the two vectors do not match up. 
metric
must be one of the following tokens :
COSINE
metric is the default metric. It calculates the cosine distane between two vectors. 
DOT
metric, also called the inner product, calculates the negated dot product of two vectors. 
EUCLIDEAN
metric, also calledL2_DISTANCE
, calculates the Euclidean distance between two vectors. 
EUCLIDEAN_SQUARED
metric, also calledL2_SQUARED
is the Euclidean distance without taking the square root. 
HAMMING
metric calculates the hamming distance between two vectors. 
MANHATTAN
metric, also calledL1_DISTANCE
or taxicab distance, calculates the Manhattan distance.

Shorthand Operators for Distances
Oracle provides the following shorthand distance operators that you can use instead of their corresponding distance functions:
<>
is the Euclidian distance operator:expr1 <> expr2
is equivalent toL2_DISTANCE(expr1, expr2)
orVECTOR_DISTANCE(expr1, expr2, EUCLIDEAN)
<=>
is the cosine distance operator:expr1 <=> expr2
is equivalent toCOSINE_DISTANCE(expr1, expr2)
orVECTOR_DISTANCE(expr1, expr2, COSINE)
<#>
is the negative dot product operator:expr1 <#> expr2
is equivalent to1*INNER_PRODUCT(expr1, expr2)
orVECTOR_DISTANCE(expr1, expr2, DOT)
Examples
VECTOR_DISTANCE
with metric EUCLIDEAN
is equivalent to L2_DISTANCE
:
VECTOR_DISTANCE(expr1, expr2, EUCLIDEAN);
L2_DISTANCE(expr1, expr2);
VECTOR_DISTANCE
with metric COSINE
is equivalent to COSINE_DISTANCE
:
VECTOR_DISTANCE(expr1, expr2, COSINE);
COSINE_DISTANCE(expr1, expr2);
VECTOR_DISTANCE
with metric DOT
is equivalent to 1 * INNER_PRODUCT
:
VECTOR_DISTANCE(expr1, expr2, DOT);
1*INNER_PRODUCT(expr1, expr2);
VECTOR_DISTANCE
with metric MANHATTAN
is equivalent to
L1_DISTANCE
:
VECTOR_DISTANCE(expr1, expr2, MANHATTAN);
L1_DISTANCE(expr1, expr2);